%2B(-2x3-x2%2B6x).jpeg "(4x3-5x2+3x)+(-2x3-x2+6x)")
Simplifying Polynomial Expressions: A Step-by-Step Guide
This article will guide you through simplifying the polynomial expression: (4x³ - 5x² + 3x) + (-2x³ - x² + 6x)
Understanding the Basics
Before we dive in, let's understand some key terms:
- Polynomial: An expression consisting of variables and coefficients, combined using addition, subtraction, and multiplication.
- Terms: Individual parts of a polynomial separated by addition or subtraction.
- Like terms: Terms with the same variable and exponent.
Simplifying the Expression
1. Remove the Parentheses:
Since we are adding the two polynomials, the parentheses don't affect the operation. We can simply rewrite the expression without them:
4x³ - 5x² + 3x - 2x³ - x² + 6x
2. Combine Like Terms:
Identify terms with the same variable and exponent. Combine their coefficients:
- x³ terms: 4x³ - 2x³ = 2x³
- x² terms: -5x² - x² = -6x²
- x terms: 3x + 6x = 9x
3. Final Simplified Expression:
After combining like terms, we arrive at the simplified expression:
2x³ - 6x² + 9x
Conclusion
By following these steps, we have successfully simplified the given polynomial expression. Simplifying expressions allows for easier manipulation and understanding of mathematical concepts. Remember to always combine like terms and follow the order of operations for accurate results.